The Wind Beneath Her Wings: Divya Tyagi’s Mathematical Genius Seeks to Explain Invisible Forces Shaping Our World

The early winter sun streamed through the windows of Penn State’s aerospace engineering building as Divya Tyagi hunched over pages of equations, her pencil moving methodically across the paper. For the fourth time that week, she had arrived before dawn to tackle what had become both her greatest challenge and passion—refining a mathematical problem that had stood largely unchanged for nearly a century.

“Some days I wondered if I was chasing an impossible solution,” Divya recalls, her voice soft but determined. “But there’s something about flight, about wind energy, that has always pulled me forward.”

In the world of aerospace engineering, Hermann Glauert’s work on wind turbine efficiency is foundational—a mathematical framework developed in the 1920s that describes how efficiently a turbine can convert wind energy into electricity. But like many pioneering works, it was incomplete.

“When Professor Schmitz first presented Glauert’s problem to me, I was intimidated,” admits Divya. “Three other students before me had attempted to expand on it without success. But there was something elegant about the mathematics that fascinated me.”

Sven Schmitz, the Boeing/A.D. Welliver Professor in Penn State’s Department of Aerospace Engineering, had been contemplating the limitations of Glauert’s approach for decades. “I always thought there had to be an easier way to approach this problem,” Schmitz explains. “When I met Divya in her junior year, I recognized the rare combination of mathematical intuition and determination that might make progress possible,” he was quoted as saying in a story by Kevin Sliman published on psu.edu.

What Divya discovered through painstaking mathematical work was that Glauert’s original formulation—while groundbreaking—focused exclusively on the maximum power coefficient without accounting for crucial parameters like thrust force and root bending moment that affect how turbine blades respond to wind pressure.

“Wind turbines don’t just need to generate electricity efficiently—they need to withstand tremendous physical forces,” Divya explains, gesturing with her hands to demonstrate. “Imagine standing with your arms outstretched while someone pushes against your palms. Your shoulders experience that bending force. Turbine blades face the same challenge on a much larger scale.”

The Breakthrough

The solution didn’t come easily or quickly. For her Schreyer Honors College thesis, Divya devoted 10 to 15 hours weekly to the problem, often working late into the night.

“The math was incredibly intensive,” she remembers. “There were moments when I thought I had the solution, only to discover a new complexity the next day. But each setback taught me something new about the physics involved.”

Her persistence ultimately led to what Schmitz describes as an “elegant solution” using calculus of variations—a mathematical method that optimizes functions within constraints. Where Glauert’s original work provided one piece of the puzzle, Divya’s addendum completed the picture, allowing engineers to understand not just power efficiency but the total aerodynamic forces affecting turbine performance.

“What makes Divya’s work so remarkable is its simplicity and usefulness,” says Schmitz. “She took something complex and made it more accessible while simultaneously expanding its applications. That’s rare in advanced mathematics.”

The practical implications are significant. As Divya explains, “Improving a large wind turbine’s power coefficient by just 1% can have enormous real-world impact—potentially generating enough additional electricity to power an entire neighborhood.” Her work provides the mathematical foundation for designing more efficient and durable wind turbines, advancing renewable energy technology at a critical time.

Now pursuing her master’s degree in aerospace engineering at Penn State, Divya has set her sights on new challenges. Her current research, supported by the U.S. Navy, involves computational fluid dynamics simulations analyzing the complex airflow around helicopter rotors as they approach naval vessels.

Recognition and Future Flight Paths

Divya’s breakthrough didn’t go unnoticed. Her thesis earned her the prestigious Anthony E. Wolk Award, presented to the aerospace engineering senior who develops the most outstanding thesis. Her research was subsequently published in Wind Energy Science, a remarkable achievement for an undergraduate student.

“Seeing my name on that published paper was surreal,” Divya says, smiling. “But what matters most to me is knowing this work might help engineers design better renewable energy systems.”

Now pursuing her master’s degree in aerospace engineering at Penn State, Divya has set her sights on new challenges. Her current research, supported by the U.S. Navy, involves computational fluid dynamics simulations analyzing the complex airflow around helicopter rotors as they approach naval vessels.

“I’m studying how the ship’s airwake interacts with a helicopter trying to land on its deck,” she explains. “It’s incredibly complex fluid dynamics, but the goal is meaningful—improving flight simulation training and ultimately pilot safety.”

In the laboratory where she conducts her computational research, Divya navigates through colorful visualizations of air turbulence patterns on her computer screen. The mathematical principles she mastered while solving Glauert’s problem now serve as foundation for this new frontier in her research.

The Human Behind the Mathematics

Despite her remarkable achievements, Divya remains humble about her contributions. Friends describe her as hardworking, thoughtful, and always willing to help fellow students grasp difficult concepts.

“Engineering isn’t just about solving problems on paper,” she reflects. “It’s about understanding how those solutions improve people’s lives.”

When not immersed in complex calculations, Divya enjoys hiking in central Pennsylvania’s mountains and volunteering with programs that encourage young women to pursue careers in STEM fields.

“I remember being a young girl fascinated by airplanes and space,” she says. “Having female mentors who showed me that aerospace engineering could be my path made all the difference. I want to be that person for the next generation.”

Looking to the Horizon

As renewable energy becomes increasingly crucial to addressing climate change, Divya’s mathematical insights may help shape the next generation of wind turbine technology. Professor Schmitz predicts her elegant solution “will find its way into classrooms across the country and around the world.”

For Divya, this is just the beginning of her journey in aerospace engineering. Whether optimizing wind energy systems or improving helicopter flight safety, she approaches each challenge with the same methodical determination that allowed her to refine Glauert’s century-old problem.

“Engineering is about persistence,” she says, looking out the window toward the sky that has always called to her. “The most important problems aren’t solved in a day or even a year. But when you finally arrive at that elegant solution—there’s nothing quite like it.”

As the sun sets over Penn State’s campus, Divya returns to her equations, already contemplating the next boundary to push, the next problem waiting for her unique perspective. In the world of aerospace engineering, her star is clearly rising—propelled by both mathematical brilliance and the willingness to tackle challenges others deemed too difficult.

And somewhere in the complex mathematics of air currents and energy efficiency, she continues to find her joy—solving the equations that help us better understand the invisible forces that shape our world.